Add & Subtract Time Calculator

Unlike standard base-10 decimal mathematics, time arithmetic operates on a sexagesimal (base-60) system inherited from ancient Babylonian astronomy. When adding time, whenever the sum of seconds reaches 60, 60 seconds are subtracted and 1 minute is carried over to the minutes column. Similarly, when minutes reach 60, 1 hour is carried over.

Formula: Total Seconds = (Hours * 3600) + (Minutes * 60) + Seconds

• Carry Rule (Addition): If Seconds ≥ 60, Seconds = Seconds mod 60, Minutes = Minutes + 1. If Minutes ≥ 60, Minutes = Minutes mod 60, Hours = Hours + 1.
• Borrow Rule (Subtraction): If Seconds < 0, Seconds = Seconds + 60, Minutes = Minutes - 1. If Minutes < 0, Minutes = Minutes + 60, Hours = Hours - 1.

• Adding Time with Base-60 Carry: (3h 45m 50s) + (2h 30m 25s) => 5h 75m 75s => 75s = 1m 15s; 76m = 1h 16m = 6 hours, 16 minutes, 15 seconds (6.2708 decimal hours)
• Subtracting Time with Base-60 Borrow: (5h 15m 10s) - (2h 40m 35s) => borrow 1m (70s - 35s = 35s); borrow 1h (74m - 40m = 34m); (4h - 2h = 2h) = 2 hours, 34 minutes, 35 seconds (2.5764 decimal hours)

Payroll timesheets, billing systems, and aviation logbooks frequently require converting sexagesimal hours and minutes into decimal hours. To convert: Decimal Hours = Hours + (Minutes / 60) + (Seconds / 3600). For example, 7 hours and 45 minutes equals 7 + (45/60) = 7.75 hours.

Formula: Decimal Hours = Hours + (Minutes / 60) + (Seconds / 3600)